Solving for Line Currents in a Wye-Delta Circuit

In summary, the conversation discusses finding three line currents using Mesh Analysis and converting a Delta Load to a Wye load. The solution involves using Zwye = (1/3)Zdelta, adding the series line impedance with the load impedance, and finding the line current using a single phase equivalent. However, the questioner is unsure why their conversion method is giving the wrong answer and asks for clarification. The solution involves transforming the Balanced Delta load to a Balance Wye load, with individual load impedances being in series with the line impedances. Ultimately, the line currents are found by dividing the phase voltages by the series line and load impedance.
  • #1
scothoward
29
0
Hi,

In the attached file, the question asks to find the three line currents. I understand the solution using Mesh Analysis that was used. However, I am unsure as to why when I convert the Delta Load to a Wye load, I get the wrong answer.

Using Zwye = (1/3)Zdelta, adding the series line impedance with the load impedance, and then finding the line current using a single phase equivalent.


Essentially the Balanced Delta load becomes a Balance Wye load of 4 + j0.666. Then the line impedances will be in series with each individual load. So each impedance should be (4 + j0.666) + (1 + j2). Finally, the line currents will be the phase voltages (100 angle0, 100 angle-120, 100 angle120) divided by the series line and load impedance, 5 + j2.666.

Am I doing something wrong?
 

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  • #2
I can't help you here, because there is no question to what need to be solve.
 
  • #3


I can understand your confusion. It is important to note that when converting a Delta load to a Wye load, the line currents will remain the same but the load currents will change. This is because the Delta load is connected in a series, while the Wye load is connected in parallel. Therefore, the line currents in both cases will be the same, but the load currents will be different.

In your calculation, you have correctly converted the Delta load to a Wye load and found the equivalent impedance. However, when finding the line currents, you have used the phase voltages divided by the series line and load impedance, which is incorrect. The correct way to find the line currents in a Wye-Delta circuit is to use the current divider rule, where the line current is equal to the load current divided by the impedance of the branch that it is connected to. In this case, the line current will be the load current of 100 angle0 divided by the impedance of (4 + j0.666) + (1 + j2). This will give you a line current of approximately 16.67 angle-18.5 degrees.

In conclusion, your approach was correct but the calculation for the line current was incorrect. By using the current divider rule, you will be able to find the correct line currents in a Wye-Delta circuit. I hope this clarifies your doubt and helps you in your future calculations. Keep up the good work!
 

FAQ: Solving for Line Currents in a Wye-Delta Circuit

1. What is a Wye-Delta Three Phase Circuit?

A Wye-Delta Three Phase Circuit is an electrical circuit that is commonly used in three-phase power systems. It consists of three branches, each containing a resistor, an inductor, and a capacitor. The circuit is named after its two configurations - the Wye (Y) configuration and the Delta (Δ) configuration.

2. What are the advantages of using a Wye-Delta Three Phase Circuit?

One of the main advantages of a Wye-Delta Three Phase Circuit is its ability to handle higher voltages and power loads. It also provides a more balanced distribution of power, making it more efficient than single-phase circuits. Additionally, the Wye-Delta configuration allows for easy grounding and isolation of one branch without affecting the other two branches.

3. How does a Wye-Delta Three Phase Circuit work?

In a Wye-Delta Three Phase Circuit, the three branches are connected in either a Wye or Delta configuration. The Wye configuration is formed by connecting one end of each component to a common point, while the Delta configuration connects each component end to the next in a triangular shape. This arrangement allows for the phases to be offset by 120 degrees, providing a smooth and consistent flow of power.

4. What are some common applications of a Wye-Delta Three Phase Circuit?

Wye-Delta Three Phase Circuits are commonly used in industrial and commercial applications, such as in motors, generators, and transformers. They are also found in power distribution systems and electric grids. Additionally, they can be used in large-scale electrical equipment, such as air conditioners, refrigerators, and other heavy-duty machinery.

5. What are some safety considerations when working with Wye-Delta Three Phase Circuits?

It is important to always follow proper safety protocols when working with any electrical circuit, including a Wye-Delta Three Phase Circuit. This may include wearing protective gear, ensuring proper grounding and isolation, and using appropriate tools and equipment. It is also crucial to have a thorough understanding of the circuit and its components before attempting to work with it.

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